This may contain some unpleasant imagery.
I was coming back from a band practice, at around 9 pm about 6 months ago. (I remembered this now because I just came the same way, and I usually return via another way.) Just after I took a left, I saw a cat try to cross the road. It stalled for a second when it saw the car coming from the other direction, but didn't have time to back up. The side of the car's wheel hit the cat. The cat didn't fly from the impact or anything. It just sort of lay down.
At first I wasn't sure if the cat was indeed hit. The other car kept on driving. I stopped to look, but it was dark, and I couldn't see very well. The cat wasn't moving. So I thought it was probably dead. And I started to drive on, but then I saw a movement from the corner of my eye, and saw the cat move its head strangely. Then it started to meow, but in such a way that I had never heard before. So I got out of the car and went over to check. I think its leg was crushed, but I could definitely see the skull had been cracked open. The cat seemed to be suffering terribly, and was moving its head in unnatural motions.
I really didn't know what to do. I wondered if it could be saved, but I really didn't think so. I was afraid to touch it. I didn't know what state it was in. So I looked for a brick of some sort to kill the cat with. I couldn't find one, so I drove on a bit, and then I found one, took it, and drove in reverse back to the cat. The cat was still wailing horribly. I got out of the car. But I couldn't do it.
Until that moment it was so obvious for me what I had to do. I had to kill the cat to put it out of its misery. But standing there with the brick in my hand, it wasn't so easy. Thoughts crept into my head :'Who was I to kill it?' I started making up excuses: 'it will probably be run over soon anyway', 'I have no right to kill it'.... I don't remember all of the excuses, but I got back in the car.
I drove forward and backward about 3 times, in indecision. Every time I drove forward, my conscience stopped me; I couldn't just leave it there. Every time I drove backward, some other part of my conscience stopped me, with all the excuses. I don't know if this whole excuses thing makes any sense to you, but I guess having another creature's life in my hands really screwed with my mind. All this time the cat was screaming. Finally I took up the courage and went over to the cat. I threw the brick forcefully on the cat's head. Then I did it again, to make sure it was dead.
I don't even know why I noded this. The feelings I had then came back all of a sudden. I'm certain I did the right thing. I only wish I did it quicker. And I hope I never have to make that decision again.
I did it again a few months ago. I was driving at night and the car opposite me stopped and I saw a form thrashing about in its headlights. The car drove away! and it took me a few seconds to realise it was a cat that was just hit. I stopped the car and got out. I looked at the cat, to see how badly it was hit, and by then it was lying on the road and twitching very slightly. It was hard to see the cat well, but he had obviously been hit in its head, and its eye was not in it's proper place. I had to decide whether it could be saved (by a vet), or not. The fact that the cat was lying very still when I came close to it, and that it was obviously a very serious head trauma left me in little doubt that there was a very slight chance, if any, of saving the cat, and that just about any vet would put it to sleep. Once I realised this, the decision to put it out of its misery was virtually instantaneous. I immediately picked up some bricks and threw them forcefully at its head and body (mostly its head), until I was sure it was dead.
The reason I decided to add this second story is to let you know that the times after the first are much easier. Well, the decision is much easier at any rate. I didn't give myself time for emotions, and I immediately knew it was the right thing to do. Once it was done, I got into my car, drove away, and after about 500 metres realised that I was shaking and stopped at the side of the road to call someone to talk to about it. I was still shaken by the experience but I am now even more certain that it was the right decision and that should the situation arise again I will not hesitate to do (what I see as) the right thing.